x^2+x=400

Simple and best practice solution for x^2+x=400 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+x=400 equation:


Simplifying
x2 + x = 400

Reorder the terms:
x + x2 = 400

Solving
x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + x + x2 = 0 + 400
x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
x + x2 = 400

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 400 + 0.25

Reorder the terms:
0.25 + x + x2 = 400 + 0.25

Combine like terms: 400 + 0.25 = 400.25
0.25 + x + x2 = 400.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 400.25

Calculate the square root of the right side: 20.006249024

Break this problem into two subproblems by setting 
(x + 0.5) equal to 20.006249024 and -20.006249024.

Subproblem 1

x + 0.5 = 20.006249024 Simplifying x + 0.5 = 20.006249024 Reorder the terms: 0.5 + x = 20.006249024 Solving 0.5 + x = 20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 20.006249024 + -0.5 x = 20.006249024 + -0.5 Combine like terms: 20.006249024 + -0.5 = 19.506249024 x = 19.506249024 Simplifying x = 19.506249024

Subproblem 2

x + 0.5 = -20.006249024 Simplifying x + 0.5 = -20.006249024 Reorder the terms: 0.5 + x = -20.006249024 Solving 0.5 + x = -20.006249024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -20.006249024 + -0.5 x = -20.006249024 + -0.5 Combine like terms: -20.006249024 + -0.5 = -20.506249024 x = -20.506249024 Simplifying x = -20.506249024

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.506249024, -20.506249024}

See similar equations:

| -16x+2x^2+24y=0 | | 15x^2-1276x+85=0 | | 25x^2-34x-343=0 | | -3p(-7)=5 | | 55x^2-127x+34=0 | | 2x^2-16x+24y=0 | | 6x-(x+9)=9+(3x-1) | | x^2=400-x | | -3p-7=5 | | (x-2)x+(2-3)3x=0 | | x^2=25x^3 | | x=25x^3 | | 5x+2(x-1)=14+3(x+2) | | 24x^2y^2-28x^2-20x^2=0 | | 5x^4=60x^3 | | 8r+5=55 | | 10x^2+7x-45=0 | | 6b(8b+8)+b(2b+3)= | | -x+y=8 | | x^2-100x^3=0 | | 3x^2+33xy+84y^2=0 | | 6x-14-24-6x=11 | | -121x^3+x^2=0 | | 4-(x-5)=2-(x+6) | | x^2-x-62=0 | | t^2-3t-40=10 | | 2x+3(x-1)=6(x+4) | | 35x^2+36x+9=0 | | 0=x^4-22x^2-75 | | 4a-5(a+1)= | | 7(4x-6)=3+(2x+1) | | 5+(6x+4)=4(2x-6) |

Equations solver categories